Longitudinal waves in a continuous transversally isotropic cylinder with initial stresses

1974 ◽  
Vol 10 (7) ◽  
pp. 775-778
Author(s):  
V. P. Kushnir
Keyword(s):  
Initial Stresses ◽  
Longitudinal Waves ◽  
Isotropic Cylinder ◽  
Transversally Isotropic

Morphological Instability of a Transversally Isotropic Solid Cylinder Under Stress

2015 ◽  
Vol 82 (3) ◽  
Author(s):  
Jérôme Colin
Keyword(s):  
Surface Diffusion ◽  
Linear Stability ◽  
Uniaxial Stress ◽  
Instability Threshold ◽  
Solid Cylinder ◽  
Morphological Instability ◽  
Isotropic Cylinder ◽  
Isotropic Solid ◽  
Transversally Isotropic

The linear stability of the surface of a transversally isotropic cylinder submitted to uniaxial stress has been theoretically investigated with respect to the development by surface diffusion of longitudinal fluctuations of its radius. The effect of stress has been characterized on the instability threshold.

scholarly journals A Mathematical Model of Longitudinal Waves Incident at a Free Surface of a Pre-Stressed Dissipative Half-Space

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2011
Author(s):  
Mahmoud M. Selim ◽  
Taher A. Nofal
Keyword(s):  
Free Surface ◽  
Reflection Coefficient ◽  
Longitudinal Wave ◽  
Initial Stress ◽  
Half Space ◽  
Seismic Waves ◽  
Initial Stresses ◽  
Reflection Coefficients ◽  
Longitudinal Waves ◽  
Stress Parameter

The aim of this work is to study the behavior of reflection of a longitudinal wave at a free surface of dissipative half-space under the effects of compressive initial stresses. When a longitudinal wave is incident on the free surface of an elastic dissipative half-space, two damped waves (Primarywaves and secondary waves are reflected. Among of these waves, P-waves are affected by compressional initial stresses. The governing equation and corresponding closed-form solutions are derived based on Biot’s incremental deformation theory. The equations of motion are solved analytically and the influence of initial stress parameter on the reflection coefficient of P-wave incidents at the free surface of dissipative half-space is studied in detail. Numerical computations are performed for actual Earth crust and the results analyzing the incident of longitudinal waves are discussed and presented graphically. The analytical solutions and numerical results reveal that the compressive initial stress parameter has notable effects on the reflection coefficient of longitudinal wave incidents on the free surface of dissipative medium. In addition, it has been observed that the presence of compressive initial stresses increases the phase velocity of the longitudinal waves. To the authors’ best knowledge, effects of compressive initial stresses on the reflection coefficients of the incident longitudinal wave on a free surface of dissipative half-space have not been studied before. Since the actual Earth is subject to initial stresses due to different resources, understanding the influences of compressive initial stresses on the reflection coefficient of a longitudinal wave helps seismologists and earthquake engineers to get accurate results of the reflection coefficients of seismic waves propagation in the Earth. Thus, the present study would be useful for seismology and earthquake engineering fields and further study about the nature of seismic waves.

scholarly journals A numerical investigation on impulse-induced nonlinear longitudinal waves in pantographic beams

2021 ◽  
pp. 108128652110108
Author(s):  
Emilio Turco ◽  
Emilio Barchiesi ◽  
Francesco dell’Isola
Keyword(s):  
Numerical Simulations ◽  
Mechanical Response ◽  
Integration Scheme ◽  
Present Contribution ◽  
Longitudinal Waves ◽  
Deformation Regime ◽  
Impulsive Loads ◽  
Unit Cells ◽  
Statics And Dynamics ◽  
Equations Of Motions

This contribution presents the results of a campaign of numerical simulations aimed at better understanding the propagation of longitudinal waves in pantographic beams within the large-deformation regime. Initially, we recall the key features of a Lagrangian discrete spring model, which was introduced in previous works and that was tested extensively as capable of accurately forecasting the mechanical response of structures based on the pantographic motif, both in statics and dynamics. Successively, a stepwise integration scheme used to solve equations of motions is briefly discussed. The key content of the present contribution concerns the thorough presentation of some selected numerical simulations, which focus in particular on the propagation of stretch profiles induced by impulsive loads. The study takes into account different tests, by varying the number of unit cells, i.e., the total length of the system, spring stiffnesses, the shape of the impulse, as well as its properties such as duration and peak amplitude, and boundary conditions. Some conjectures about the form of traveling waves are formulated, to be confirmed by both further numerical simulations and analytical investigations.

Coupled flexural-longitudinal waves in an origami metamaterial with uncoupled creases

2021 ◽  
Vol 396 ◽  
pp. 127232
Author(s):  
Zhu-Long Xu ◽  
Shao-Feng Xu ◽  
Kuo-Chih Chuang
Keyword(s):  
Longitudinal Waves
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